In Johnny’s Physics class, they were tasked to think and suggest a way to make a stainless-steel spoon float on water using the following materials only –stainless steel spoon, a container of water, and a supply of olive oil. Jim, who is Johnny’s groupmate, suggested to coat the spoon with olive oil. Jim reasoned that this would work since olive oil is less dense than water, the spoon will float on the surface of the water with the olive oil.

Hearing Jim’s explanation, Johnny was doubtful if Jim’s suggestion would really work.

If you were Johnny’s groupmate, using your understanding of the Physics you learned, write an explanation whether Jim’s suggestion would work or not.

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Explain what it means to view something from a frame of reference. provide an example that illustrates your explanation. (4 points)